1-Prove the identity.
cosh(x) + sinh(x) = ex
| cosh(x) + sinh(x) | = | ex + e?x+ |
|
| = | |
|
| = | |
2-Prove the identity.
sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)
| sinh(x) cosh(y) + cosh(x) sinh(y) | = | (ex ? e?x) +(ex + e?x) |
|
| = | + ex ? y ? e?x + y ? e?x ?y+ex + y ? ex ? y + e?x + y ?e?x ? y |
|
| = | ? 2e?x ? y |
|
| = | ex + y ? e?(x + y) |
|
| = | |
3-Prove the identity.
sinh(2x) = 2 sinh(x) cosh(x)
| sinh(2x) | = | sinhx + |
|
| = | sinh(x) + cosh(x) sinh(x) |
|
| = | |
4-Prove the identity.
= e2x
| = | |
|
| = | |
|
| = | | ex + e?x+(ex ? e?x | | ex + e?x?(ex ? e?x |
|
|
| = | |
|
| = | |
5-If
tanh(x) =
,
find the values of the other hyperbolic functions atx.
| sinh(x) | = | |
| cosh(x) | = | |
| coth(x) | = | |
| sech(x) | = | |
| csch(x) | = | |
